Ratio and proportion word problems, step by step
A ratio is how a story compares two amounts, and a proportion is what lets you scale it.
The question
At that rate, how long will it take to stamp 300 tickets?
A press stamps 200 tickets every 4 minutes.
200 ÷ 4 = 50
200 ÷ 4 = 50
300 ÷ 50 = 6 minutes
asked:At that rate, how long will it take to stamp 300 tickets?
6 minutes
- Read it through once. Two things change TOGETHER at a fixed rate, so the trick is to find the rate for ONE unit first — everything the question asks scales from that.
- Find the rate for one: 200 ÷ 4 = 50. That is how much goes with a single unit.
- Now scale that rate of 50 to what the question asks: 300 ÷ 50 = 6 minutes.
- Answer the question that was asked — "At that rate, how long will it take to stamp 300 tickets?" — 6 minutes.
How it works.
- 01
Read it through once. Two things change TOGETHER at a fixed rate, so the trick is to find the rate for ONE unit first — everything the question asks scales from that.
- 02
Find the rate for one: 200 ÷ 4 = 50. That is how much goes with a single unit.
- 03
Now scale that rate of 50 to what the question asks: 300 ÷ 50 = 6 minutes.
- 04
Answer the question that was asked — "At that rate, how long will it take to stamp 300 tickets?" — 6 minutes.